In another bowl, cream the butter, sugar and vanilla with an electric mixer. Add the egg and beat until smooth. At low speed or with a wooden spoon, stir in the dry ingredients. Shape the dough into 2 discs. Cover in plastic wrap and refrigerate for 1 hour.
With the rack in the middle position, preheat oven to 350 °F (180 °C). Line two baking sheet with parchment paper or silicone mats.
On a lightly floured work surface, roll out one disc of dough at a time, to a1 /4 inch (5 mm) thick sheet. Cut out cookies using cookie cutters. Spread them on the prepared sheets. Reuse scrap.
Bake, one sheet at a time, for about 12 minutes or until lightly browned. Let cool completely.
Decorate with royal icing, if desired (see recipe). Allow the icing to set before stacking 3D parts. Store in an airtight container at room temperature for up to 3 weeks or freeze.